"...why shouldn't everyone climb the mountains? "
Well, as a general principle I'm all in favour of access to the mountains, but in the case of everest, there is a big problem with the sheer volume of people attempting it - just look at the mess at base camp, the queues for the summit, the litter at the South Col, etc...
Clearly something has to be done to limit numbers. I'm not really keen on the current approach of making it prohibitively expensive for the vast majority, because it seems like a rather artificial barrier to entry. I'd personally much rather see a rule like "no oxygen" - which would cut out 80-90% of the punters at a stroke, and would hopefully increase the skill level on the hill as well, which has to be a good thing from an accident prevention point of view ( If 'Thin Air' is to be beleived, a large proportion of everest fatalities stem from people who are relying on oxygen having their oxygen supplies fail.)
Of course, this means that mortals like me, and (I guess) you, wouldn't have a chance to do it. But so what? There are gazillions of smaller peaks that are just as challenging and as beautiful, if not more, so we can go and climb them instead.
I suppose the more serioius down side to this approach is that the revenue generated from expeditions must be a significant source of funding to the Nepalese government, and not something they would want to give up lightly - so I don't imagine things will change too soon